Question

1. The price of a book decreased from #25 to #20. By how many percent did the price decrease?

a. 5
b. 10
c. 20
d. 25

2. After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian had answered 150 questions correctly, how many correct answers did he answer in the second test?

a. 105
b. 120
c. 180
d. 195

3. A number is increased by 2 and then multiplied by 3. The result is 24. What is this number?

a. 4
b. 6
c. 8
d. 10

4. My father’s age divided by 5 is equal to my brother’s age divided by 3. My brother is 3 years older than me. My father’s age is 3 less than 2 times my age. How old is my father?

a. 34
b. 45
c. 56
d. 61

5. (x – 2) / 4 – (3x + 5) / 7 = – 3, x = ?

a. 6
b. 7
c. 10
d. 13​

Answer 1

(1) C

(2) D

(3) B

(4) B

(5) C

Explanation:

(1) % decrease = change in price/initial price × 100 = (25 -20)/25 × 100 = 5/25 × 100 = 20

(2) Number of correct answers he answered in the second test = 150 + (30/100 × 150) = 150 + 45 = 195

(3) Let the number be y

3(y + 2) = 24

y + 2 = 24/3 = 8

y + 2 = 8

y = 8 - 2 = 6

(4) Let my father's age be f, my brother's age be b and my age be m

From the first statement

f/5 = b/3 ----- eqn (1)

From the second statement

b = m + 3 ----- eqn (2)

From the third statement

f = 2m - 3 ------ eqn (3)

Substitute the expression of b and f in eqn 2 & 3 into eqn 1

(2m - 3)/5 = (m + 3)/3

3(2m - 3) = 5(m + 3)

6m - 9 = 5m + 15

6m - 5m = 15 + 9

m = 24

Substitute the value of m into eqn 3

f = 2m - 3 = 2(24) - 3 = 48 - 3 = 45

(5) (x - 2)/4 - (3x + 5)/7 = -3

The LCM of 4 and 7 is 28

Multiply each term in the equation by 28

7(x - 2) -4(3x + 5) = -3(28)

7x - 14 - 12x - 20 = -84

-5x - 34 = -84

-5x = -84 + 34

-5x = -50

x = -50/-5 = 10